2024/12/07 by Eduardo Schirmer Finn, Finn, Eduardo Schirmer, Eduardo Horta +1
Engineering · Chemistry · #Fault Detection and Control Systems #Machine Fault Diagnosis Techniques #Spectroscopy and Chemometric Analyses
paper · pdf · doi:10.48550/arxiv.2412.05736
For highly skewed or fat-tailed distributions, mean or median-based methods often fail to capture the central tendencies in the data. Despite being a viable alternative, estimating the conditional mode given certain covariates (or mode regression) presents significant challenges. Nonparametric approaches suffer from the "curse of dimensionality", while semiparametric strategies often lead to non-convex optimization problems. In order to avoid these issues, we propose a novel mode regression estimator that relies on an intermediate step of inverting the conditional quantile density. In contrast to existing approaches, we employ a convolution-type smoothed variant of the quantile regression. Our estimator converges uniformly over the design points of the covariates and, unlike previous quantile-based mode regressions, is uniform with respect to the smoothing bandwidth. Additionally, the Convolution Mode Regression is dimension-free, carries no issues regarding optimization and preliminary simulations suggest the estimator is normally distributed in finite samples.